Type-amalgamation properties and polygroupoids in stable theories-Reference-Cited by-同舟云学术

Type-amalgamation properties and polygroupoids in stable theories

Published:2015-06 Issue:01 Volume:15 Page:1550004
ISSN:0219-0613
Container-title:Journal of Mathematical Logic
language:en
Short-container-title:J. Math. Log.

Author:

Goodrick John¹,Kim Byunghan²,Kolesnikov Alexei³

Affiliation:

1. Department of Mathematics, Universidad de los Andes, Carrera 1 No. 18A-12, Bogotá, Colombia

2. Department of Mathematics, Yonsei University, 50 Yonsei-ro, Seodaemun-gu, Seoul 120-749, Republic of Korea

3. Department of Mathematics, Towson University, 7800 York Road, Towson, MD 21252, USA

Abstract

We show that in a stable first-order theory, the failure of higher dimensional type amalgamation can always be witnessed by algebraic structures that we call n-ary polygroupoids. This generalizes a result of Hrushovski in [16] that failures of 4-amalgamation are witnessed by definable groupoids (which correspond to 2-ary polygroupoids in our terminology). The n-ary polygroupoids are definable in a mild expansion of the language (adding a predicate for a Morley sequence).

Publisher

World Scientific Pub Co Pte Lt

Subject

Logic

Link

https://www.worldscientific.com/doi/pdf/10.1142/S021906131550004X

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